Linear Vibration And Buckling Analysis Of Functionally Graded Piezoelectric Nanobeams

Piezoelectric materials can produce charge under external loads, whereas under applied electric field they can produce stress or mechanical movement. With the application of piezoelectric micro-/nano-material and development of preparation technology of materials, low dimensional piezoelectric nanostructures have attracted extensive attention. Piezoelectric nano-materials not only have coupled mechanical and electrical properties, but also demonstrate many characteristics in mechanics, electrics, magnetics, acoustics and optics etc, so they are widely used in various types of nano-devices.Functionally graded materials (FGMs) are new composite materials, which are used of advanced composite technology, making the composition and structure of the material gradient change along the thickness direction. They can improve the stress distribution, reduce the stress concentration, improve the fracture toughness, enhance resistance to heat, therefore FGMs have important value of application in many engineering fields.A lot of experiments and numerical simulations show that:when the proper length of the materials arrives at the magnitude of micro-/nano-scales, the size effect will be obvious. The classical theory of elasticity constitutive relation does not contain any associated with the scale parameter, so this theory can’t be used to describe and predict the phenomenon of size effect of nano-structures. At present, the high order continuous medium theory (such as the nonlocal elasticity theory, the surface elasticity) is considered the most simple and effective method to simulate the mechanical properties of nano-structures.Based on the Eringen’s nonlocal elasticity theory, the functionally graded piezoelectric Timoshenko nanobeam models are established. Size effect on the vibration and buckling behaviors is studied. Main contents of this work are as follows:(1)Based on the nonlocal theory, the functionally graded piezoelectric nanobeam model is established. Under the boundary conditions of hinged-hinged and clamped-clamped and hinged-clamped, the influence of the nonlocal parameter, the slenderness rate and the gradient index on the linear vibration of beam is studied.(2)Using the functionally graded piezoelectric nanobeam model, the influence of the nonlocal parameter, the slenderness rate and the gradient index on the buckling of beam is studied.In the theoretical analysis and mathematical derivation, the Hamilton principle is used in deriving the governing equations and the corresponding boundary conditions. The differential quadrature method (DQM) is used to discretize the governing equations, which are then solved numerically.